Mathematics, 26.04.2020 05:02 aramirez4785

Arup says: if a b is fully simplified, then b must be a prime number. Val says that if a b has b as a prime number, then the expression is fully simplified. Who is right? Or are both or neither of them right? Show/explain and FIX any wrong statements to be correct, with evidence.

Answers: 2

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Answer from: kimloveswim

Neither is correct

If a/b is fully simplified, then we cannot reduce the fraction further. One example is 2/7 which has b = 7 being prime. So far Arup is correct; however, we could have 3/10 as another example of an irreducible fraction with b = 10 this time and it is not prime (10 = 2*5). This is one of infinitely many counter-examples to disprove Arup's claim.

Val's claim is not correct either. Let's make b some prime number. For example lets make b = 11. Double this value to get 2*11 = 22 and we'll make this the value of 'a'. So a = 22. Then note how a/b = 22/11 = 2/1. I've shown that if b = 11, then it is possible to have a/b equal to a fraction that hasn't been fully reduced. The prime requirement on b is not necessary. Instead, we must ensure that 'a' and 'b' together do not have any common factors, which is what leads to fraction reduction. For more information, look up the term "relatively prime" or "coprime".

Answer from: Quest

location: point 0

step-by-step explanation:

well, -8 to 10 on a number line is 18 spaces.

1/9 of 18 is 2.

so, 4/9 of 18 must be 8.

8 spaces from -8 (a) is 0.

so, 4/9 of the way from -8 to 10 is 0!

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is